Half of a Riordan array and restricted lattice paths

DOI10.1016/j.laa.2017.09.027zbMath1373.05007OpenAlexW2756688589MaRDI QIDQ1675653

Juan Yin, Sheng-Liang Yang, Yan-Ni Dong, Lin Yang

Publication date: 2 November 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2017.09.027

zbMATH Keywords

generating functionCatalan numbersRiordan arrayLukasiewicz pathcentral coefficients

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Theory of matrix inversion and generalized inverses (15A09) Permutations, words, matrices (05A05) Matrices of integers (15B36) Matrices, determinants in number theory (11C20)

Related Items (19)

Unnamed Item ⋮ On the halves of double and 3-dimensional Riordan arrays ⋮ Commutators and commutator subgroups of the Riordan group ⋮ The halves of Delannoy matrix and Chung-Feller properties of the \(m\)-Schröder paths ⋮ Half Riordan array sequences ⋮ The halves of a 3-dimensional Riordan array ⋮ Generalized Delannoy matrices and their combinatorial properties ⋮ The skew halves of a Riordan array ⋮ The research and progress of the enumeration of lattice paths ⋮ Riordan arrays and difference equations of subdiagonal lattice paths ⋮ Unnamed Item ⋮ Generalized Schröder matrices arising from enumeration of lattice paths ⋮ Combinatorial matrices derived from generalized Motzkin paths ⋮ Riordan arrays, Łukasiewicz paths and Narayana polynomials ⋮ Enumeration of lattice paths with infinite types of steps and the Chung-Feller property ⋮ A Chung-Feller property for the generalized Schröder paths ⋮ The group generated by Riordan involutions ⋮ Enumerating several aspects of non-decreasing Dyck paths ⋮ On the halves of a Riordan array and their antecedents

Cites Work

• Combinatorial sums through Riordan arrays
• Combinatorics of Riordan arrays with identical \(A\) and \(Z\) sequences
• Identities induced by Riordan arrays
• Some identities on the Catalan, Motzkin and Schröder numbers
• Sequence characterization of Riordan arrays
• The Riordan group
• A Catalan triangle
• Pascal triangles, Catalan numbers and renewal arrays
• On the \(r\)-shifted central coefficients of Riordan matrices
• Parametric Catalan numbers and Catalan triangles
• A divisibility property for a subgroup of Riordan matrices
• Generating trees and proper Riordan arrays
• Schröder matrix as inverse of Delannoy matrix
• A Method for Obtaining Generating Function for Central Coefficients of Triangles
• Motzkin numbers
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